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arXiv:1402.2276 · Physical Review A

Measurement of the Kerr nonlinear refractive index of Cs vapor

M. Araujo, Hugo L. D. de S. Cavalcante, Marcos Oriá, Martine Chevrollier, Thierry Passerat de Silans, Romeu Castro, D. Moretti

Published Dec 10, 2013• 17 citations
arXivHTMLPDF

Abstract

Atomic vapors are systems well suited for nonlinear optics studies but very few direct measurements of their nonlinear refractive index have been reported. Here we use the $z$-scan technique to measure the Kerr coefficient, ${n}_{2}$, for a Cs vapor. Our results are analyzed through a four-level model, and we show that coherence between excited levels as well as cross-population effects contribute to the Kerr nonlinearity.

DOI
10.1103/physreva.88.063818

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Atomic vapors are systems well suited for nonlinear optics studies but very few direct measurements of their nonlinear refractive index have been reported. Here we use the zzz-scan technique to measure the Kerr coefficient, n2{n}_{2}n2​, for a Cs vapor. Our results are analyzed through a four-level model, and we show that coherence between excited levels as well as cross-population effects contribute to the Kerr nonlinearity.
We report the measurement of the Kerr nonlinear refractive index of the rubidium vapor via the high sensitivity z-scan method by using an optical frequency comb. The novel self-focusing and self-defocusing effects of the vapor are presented with red and blue detunings of the laser frequency. The optical nonlinear characteristics of the rubidium vapor are clearly interpreted under different experimental parameters. Furthermore, the Kerr nonlinear refractive index n2 is obtained from the measured dispersion curve, and it basically occurs on the order of 10−6 cm2/W. The evolutions of the Kerr nonlinear coefficient n2 with the laser power and frequency detuning, respectively, are studied. To the best of our knowledge, the use of pulsed lasers to measure the Kerr nonlinear refractive index n2 of atomic vapor has not been reported yet. The direct measurement of the Kerr nonlinear coefficient will greatly help us understand and optimize nonlinear optical processes and find its more potential applications in quantum optics.
Atomic vapors make flexible and useful nonlinear optical media when light is detuned far from resonances. However, few direct measurements of their nonlinear coefficients have been performed to date. We present a measurement of the Kerr coefficient for various detunings to both the red and blue of the D2D2D2 line in hot atomic rubidium vapor. Saturation effects complicate the interpretation of the standard z-scan method, but a simple saturation model agrees well with our data. We find values of ${n}_{2}\ensuremath{\approx}\ifmmode\pm\else\textpm\fi{}{10}^{\ensuremath{-}7}{\mathrm{cm}}^{2}/\mathrm{W}$ for 1 GHz detunings from the D2D2D2 line.
The potential to precisely control both the linear and nonlinear index of refraction through optical manipulation of the atomic states has recently pushed warm alkali vapors to the forefront of research in the field of quantum sensors, quantum memories, and quantum fluids of light. Rubidium (Rb) vapor in centimeter-scale glass cells or millimeter-scale MEMS cells has proven to be a very promising platform for these applications, yet only a handful of research works have been dedicated to the investigation of the (non)linear refractive index of Rb vapor. We present results of theoretical calculations of the (non)linear refractive index of warm Rb vapor, based on the optical Bloch equations for 6-level Rb atoms interacting with a probe laser. They are compared to the experimental results obtained using an interferometric technique, showing excellent quantitative agreement. A Kerr nonlinear refractive index n2n_2n2​ of up to 10−410^{-4}10−4 cm2^22/W is obtained. Python scripts for all theoretical calculations presented in this work are provided, including the refractive index calculation, that can readily be used in practical implementations for simulating the (non)linear refractive index of Rb vapor including the effects of Doppler broadening, transit time broadening, pressure broadening, saturation, optical pumping, and spin-exchange collisions.
Summary form only given. We present our recent results in measuring the nonlinear Kerr index of refraction of multi-level rubidium atoms inside an optical ring cavity. By using a similar experimental arrangement as we used previously to demonstrate cavity linewidth narrowing due to EIT inside an optical ring cavity, we can measure the nonlinear coefficient χ/sup (3)/ through the asymmetric transmission profile of the ring cavity. By measuring the degree of asymmetry, we can obtain the Kerr nonlinear index of refraction directly, without worrying about contributions from linear absorption. Our preliminary results indicate a significant enhancement of Kerr nonlinearity due to atomic coherence at near-resonance conditions. We present our experimental results and their comparison with theoretical calculations. We discuss the implications of this enhanced nonlinear Kerr index of refraction to nonlinear optical processes in an optical cavity.
The potential to precisely control both the linear and nonlinear index of refraction through optical manipulation of the atomic states has recently pushed warm alkali vapors to the forefront of research in the field of quantum sensors, quantum memories, and quantum fluids of light. Rubidium (Rb) vapor in centimeter-scale glass cells or millimeter-scale micro-electro-mechanical system (MEMS) cells has proven to be a very promising platform for these applications, yet only a handful of research works have been dedicated to the investigation of the (non)linear refractive index of Rb vapor. We present results of theoretical calculations of the (non)linear refractive index of warm Rb vapor, based on the optical Bloch equations for 6-level Rb atoms interacting with a probe laser. They are compared to the experimental results obtained using an interferometric technique, showing very good quantitative agreement. A Kerr nonlinear refractive index n2 of up to −1.2×10−4 cm2/W is obtained. Python scripts for all theoretical calculations presented in this work are provided, including the refractive index calculation, that can readily be used in practical implementations for simulating the (non)linear refractive index of Rb vapor including the effects of Doppler broadening, transit time broadening, pressure broadening, saturation, optical pumping, and spin-exchange collisions.